Related papers: Comparison of connectivity and rigidity percolatio…
Contraction analysis considers the distance between two adjacent trajectories. If this distance is contracting, then trajectories have the same long-term behavior. The main advantage of this analysis is that it is independent of the…
Understanding how network structure constrains and enables information processing is a central problem in the statistical mechanics of interacting systems. Here we study random networks across the structural percolation transition and…
Dimensionality reduction is a crucial technique in data analysis, as it allows for the efficient visualization and understanding of high-dimensional datasets. The circular coordinate is one of the topological data analysis techniques…
Usually, density functional models are considered approximations to density functional theory, However, there is no systematic connection between the two, and this can make us doubt about a linkage. This attitude can be further enforced by…
We investigate the geometric properties of loops on two-dimensional lattice graphs, where edge weights are drawn from a distribution that allows for positive and negative weights. We are interested in the appearance of spanning loops of…
We introduce a formalism for computing bond percolation properties of a class of correlated and clustered random graphs. This class of graphs is a generalization of the Configuration Model where nodes of different types are connected via…
Many real complex systems cannot be represented by a single network, but due to multiple sub-systems and types of interactions, must be represented as a multiplex network. This is a set of nodes which exist in several layers, with each…
Variational inequalities are an important tool, which includes minimization, saddles, games, fixed-point problems. Modern large-scale and computationally expensive practical applications make distributed methods for solving these problems…
Rigidity analysis using the "pebble game" has been applied to protein crystal structures to obtain information on protein folding, assembly and t he structure-function relationship. However, previous work using this technique has not made…
We present an exact mathematical framework able to describe site-percolation transitions in real multiplex networks. Specifically, we consider the average percolation diagram valid over an infinite number of random configurations where…
The problem of continuum percolation in dispersions of rods is reformulated in terms of weighted random geometric graphs. Nodes (or sites or vertices) in the graph represent spatial locations occupied by the centers of the rods. The…
Separation Logic is a widely used formalism for describing dynamically allocated linked data structures, such as lists, trees, etc. The decidability status of various fragments of the logic constitutes a long standing open problem. Current…
We show the equivalence of several notions in the theory of taut foliations and the theory of tight contact structures. We prove equivalence, in certain cases, of existence of tight contact structures and taut foliations.
We analytically study proximity and distance properties of various kernels and similarity measures on graphs. This helps to understand the mathematical nature of such measures and can potentially be useful for recommending the adoption of…
A wide variety of methods have been used to compute percolation thresholds. In lattice percolation, the most powerful of these methods consists of microcanonical simulations using the union-find algorithm to efficiently determine the…
We address the problem of efficiently gathering correlated data from a wired or a wireless sensor network, with the aim of designing algorithms with provable optimality guarantees, and understanding how close we can get to the known…
We introduce models of generic rigidity percolation in two dimensions on hierarchical networks, and solve them exactly by means of a renormalization transformation. We then study how the possibility for the network to self organize in order…
In this work, water distribution systems are regarded as large sparse planar graphs with complex network characteristics and the relationship between important topological features of the network (i.e. structural robustness and loop…
We study the design of efficient algorithms for combinatorial pattern matching. More concretely, we study algorithms for tree matching, string matching, and string matching in compressed texts.
This paper provides a theoretical and computational justification of the long held claim that of the similarity of the probit and logit link functions often used in binary classification. Despite this widespread recognition of the strong…